I agree that duplication is not standard probability. Standard probability has no notion of an indexical so these situations end up overlapping.
There are two routes here as per A tree falls on sleeping beauty. One is to go the halver route and handle duplications in the decision theory. The other is to go the thirder route and construct what I’ll call an agent-state relative probability. Roughly, I mean a notion of probability that is concerned more with what fraction of agent-states will be correct than with any objective notion of probability. As I explained on my comment to the paradoxes post, we shouldn’t be surprised that a notion of probability specifically designed to be relative in this sense will be relative to what agents exist. So I’m more than happy to bite the bullet on the reductio ad absurdum.
I agree that duplication is not standard probability. Standard probability has no notion of an indexical so these situations end up overlapping.
There are two routes here as per A tree falls on sleeping beauty. One is to go the halver route and handle duplications in the decision theory. The other is to go the thirder route and construct what I’ll call an agent-state relative probability. Roughly, I mean a notion of probability that is concerned more with what fraction of agent-states will be correct than with any objective notion of probability. As I explained on my comment to the paradoxes post, we shouldn’t be surprised that a notion of probability specifically designed to be relative in this sense will be relative to what agents exist. So I’m more than happy to bite the bullet on the reductio ad absurdum.